Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present a series of one- and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective-dispersive transport with mass exchange into dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.
Contaminant transport processes in streams, rivers, and other surface water bodies can be analyzed or predicted using the advection-dispersion equation and related transport models. In part 1 of this two-part series we presented a large number of one- and multi-dimensional analytical solutions of the standard equilibrium advection-dispersion equation (ADE) with and without terms accounting for zero-order production and first-order decay. The solutions are extended in the current part 2 to advective-dispersive transport with simultaneous first-order mass exchange between the stream or river and zones with dead water (transient storage models), and to problems involving longitudinal advectivedispersive transport with simultaneous diffusion in fluvial sediments or near-stream subsurface regions comprising a hyporheic zone. Part 2 also provides solutions for one-dimensional advective-dispersive transport of contaminants subject to consecutive decay chain reactions.
We find an exact asymptotic formula for the singular values of the integral operator of the form $\int _{\Omega } T(x,y)k(x-y) \cdot \mathrm{d}y \: L^2 (\Omega )\rightarrow L^2(\Omega)$ ($\Omega \subset \mathbb{R}^m$, a Jordan measurable set) where $k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{\frac{m}{2}})$, $k_0 (x) = x^{\alpha -1} L(\tfrac{1}{x})$, $\tfrac{1}{2} - \tfrac{1}{2m}< \alpha < \tfrac{1}{2}$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$.
In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three-dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2].
In response to the scholar debate regarding the way in which Great Moravian spherical buttons were used, this study presents an overview of specimens whose use may be inferred on the basis of the archaeological context. The topic is demonstrated using two case studies, where the function of the spherical buttons may be definitively proved thanks to preserved textile fibres. Textile and metal material characterization was performed by EDS analysis on SEM. The case studies are accompanied by analogous finds known from the literature. In conclusion, we propose possible interpretations of the functional range of spherical hollow buttons.
This paper describes the dynamic modeling of nonholonomic system for control purposes. The equations of motion together with nonholonomic constraint are reduced into system of five 1st order equations. Further, the exact linearization is performed and finally we obtain a decoupled system of two independent integrator chains. Next we describe the controller design, and at the end, the simualtion results are presented. and Obsahuje seznam literatury
The failure time distribution for various items often follows a shifted (two-parameter) exponential model and not the traditional (one-parameter) exponential model. The shifted exponential is very useful in practice, in particular in the engineering, biomedical sciences and industrial quality control when modeling time to event or survival data. The open problem of simultaneous testing for differences in origin and scale parameters of two shifted exponential distributions is addressed. Two exact tests are proposed using maximum likelihood estimators. They are based on the combination of two statistics following a maximum-type and a distance-type approach. The exact null distributions of the respective test statistics are derived analytically. Small sample type-one error rate and power of the tests are studied numerically. We showed that the test based on the maximum type combination (the Max test) should be preferred being generally more powerful than the test based on the distance type combination (the Distance test). An application to a biomedical experiment is discussed.
Hydrological processes research remains a field that is severely measurement limited. While conventional tracers (geochemicals, isotopes) have brought extremely valuable insights into water source and flowpaths, they nonetheless have limitations that clearly constrain their range of application. Integrating hydrology and ecology in catchment science has been repeatedly advocated as offering potential for interdisciplinary studies that are eventually to provide a holistic view of catchment functioning. In this context, aerial diatoms have been shown to have the potential for detecting of the onset/cessation of rapid water flowpaths within the hillslope-riparian zone-stream continuum. However, many open questions prevail as to aerial diatom reservoir size, depletion and recovery, as well as to their mobilisation and transport processes. Moreover, aerial diatoms remain poorly known compared to freshwater species and new species are still being discovered. Here, we ask whether aerial diatom flushing can be observed in three catchments with contrasting physiographic characteristics in Luxembourg, Oregon (USA) and Slovakia. This is a prerequisite for qualifying aerial diatoms as a robust indicator of the onset/cessation of rapid water flowpaths across a wider range of physiographical contexts. One species in particular, (Hantzschia amphioxys (Ehr.) Grunow), was found to be common to the three investigated catchments. Aerial diatom species were flushed, in different relative proportions, to the river network during rainfall-runoff events in all three catchments. Our take-away message from this preliminary examination is that aerial diatoms appear to have a potential for tracing episodic hydrological connectivity through a wider range of physiographic contexts and therefore serve as a complementary tool to conventional hydrological tracers.
The time profiles of the solar microwave emission exhibit various phenomona reflecting the evolution of magnetic flux tubes before and during the onset of flare events. Different scenarios are posslble to describe the processes of energy release in a flux tube and the interaction of a number of tubes during the preflare stage and the early flare development, Multi-peak structures at quite
different time scales displayed by flux records at mm-, cm-, and dm-waves are examined; they rise the question how to distinguish between repeated energy release at one site and the propagation of the flare disturbances over an extended source area, A discussion of observed time scales and released energy in the frame of some scenarios is carried out.
We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.